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Let X ~ Geom(p), let n be a non-negative integer, and let

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 17E Chapter 4.4

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 17E Problem 17E

Let X ~ Geom(p), let n be a non-negative integer, and let Y ~ Bin(n, p). Show that P(X = n) = (l/n)(1/n)p(Y=1).

Step-by-Step Solution:

Solution :

Step 1 of 1:

Given and

Where mean  and variance .

Here non-negative integer is n.

Our goal is :

We need to prove that P(X=n)=.

Now we have to prove that P(X=n)=.

P(X=n)=

The formula of the geometric distribution is

P(X=n)=

Where q = (1-p)

So P(X=n)=

Then,

P(X=n)=

The formula of the binomial distribution is

Here the probability of X is n and the probability of Y is 1.

P(X=n)=

Here and = p.

P(X=n)=

Therefore P(X=n)=.


Step 2 of 1

Chapter 4.4, Problem 17E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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Let X ~ Geom(p), let n be a non-negative integer, and let